Continuous Random Variables

Overview

This course covers the learning outcomes and goals of understanding continuous random variables, probability density functions, cumulative distribution functions, expectations, variances, and various continuous distributions. The course teaches skills such as analyzing continuous random variables, calculating expectations and variances, and applying different continuous distributions. The teaching method involves theoretical explanations and mathematical examples. The intended audience for this course includes students and professionals interested in probability theory and statistics.

Syllabus

An Introduction to Continuous Random Variables and Probability Density Functions.
The Uniform Distribution.
Notes on Continuous Random Variables' Probability Density Functions.
Cumulative Distribution Functions for Continuous Random Variables.
Connecting Probability Density Functions and Cumulative Distribution Functions.
Expectation of a Continuous Random Variable.
Expectation of a Function of a Continuous Random Variable.
Variance of a Random Variable.
Variance (Continuous Example).
Exponential Distribution Basics.
Gamma Basics.
Chi-Squared Basics.
Normal Distribution Basics.